Graham effusion time calculator
If a gas of 4 g/mol takes 10 seconds to effuse, a gas of 16 g/mol takes 20 seconds under the same conditions. Enter the reference time and both molar masses to get the second time and the time ratio. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Time ref
- 10
- Molar mass ref
- 4
- Molar mass
- 16
- Time
- 20
- Time ratio
- 2
- Rate ratio
- 2
Graham’s law of effusion links how quickly gases pass through a tiny pinhole to their molar masses: under the same temperature and pressure, the ratio of effusion rates equals the inverse square root of the molar-mass ratio, so the times needed to effuse equal amounts scale as the square root of the molar masses themselves. Students comparing hydrogen to oxygen on a worksheet, lab instructors grading timed-effusion experiments, process engineers sketching leak and purge estimates, and tutoring platforms that need a stable oracle all want the same contract—a positive reference effusion time, two positive molar masses in matching units, and a structured second-gas time without re-deriving the square-root formula by hand.
What Graham effusion time means and which inputs you must send
In introductory chemistry, Graham’s law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
When two gases are compared under identical conditions, rate one over rate two equals the square root of M two over M one; because time to effuse a fixed amount is inversely proportional to rate, the time form students actually search for is t two over t one equals the square root of M two over M one, or t two equals t one times that square root.
Search intent clusters around graham effusion time calculator, graham law of effusion molar mass, gas effusion time ratio, compare hydrogen oxygen effusion times, and t2 from molar mass. People want a numeric answer they can check against a lab report, embed in a homework key, or feed into a larger pipeline—not only a reminder that the formula exists. Keep units consistent: the engine multiplies and takes a square root only; it does not convert minutes to seconds or grams per mole to kilograms per mole.
Zero molar mass for either gas is always rejected because the ratio under the square root becomes undefined or infinite for this product, and negative masses or non-positive reference times are rejected so the contract stays honest for laboratory work.
How this calculator validates inputs and applies t2 = t1 √(M2/M1)
Numeric strings that parse to finite numbers are accepted so web forms and CSV-style pipelines can pass values without an extra cast. Both molar masses must be strictly positive and must not be zero—the product contract names zero molar mass as the hard invalid case for either gas. Reference time must be strictly positive.
There is no real-gas correction, no temperature or pressure dependence beyond the ideal Graham premise, and no unit conversion service—this is pure Graham for equal-condition effusion times. Heavier second gases produce longer times than the reference; lighter second gases produce shorter times, matching the physical intuition that light molecules effuse faster.
What you can do with it
Homework and timed-effusion drills
Students and graders convert a measured reference effusion time and two molar masses into the second gas’s expected time, with clear rejection when a molar mass is zero by mistake.
Lab notebook and curriculum sketches
Quick structured estimates of comparative effusion times for light and heavy gases without standing up a full process simulator or spreadsheet.
FAQ
What happens if a molar mass is zero?
Zero molar mass makes √(M2/M1) undefined or infinite for this product; both molar masses must be strictly positive and are not charged on failure.
Does a heavier gas take longer to effuse?
Yes under Graham’s law at equal conditions: if M2 is greater than M1, t2 is greater than t1. Lighter second gases produce shorter effusion times than the reference.
Is the graham effusion time calculator free?
The browser tool runs free on your device.
Does the calculator convert time or molar-mass units?
The engine multiplies and takes a square root only.
How is effusion time different from effusion rate?
They are inverses. A faster rate means a shorter time for the same amount of gas, so times grow with the square root of the molar masses while rates shrink with it.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/graham-effusion-time \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"time_ref":30,"molar_mass_ref":2.016,"molar_mass":32}'const res = await fetch("https://api.kit.forhosting.com/chem/graham-effusion-time", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"time_ref": 30,
"molar_mass_ref": 2.016,
"molar_mass": 32
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/graham-effusion-time",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"time_ref": 30,
"molar_mass_ref": 2.016,
"molar_mass": 32
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/graham-effusion-time", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"time_ref":30,"molar_mass_ref":2.016,"molar_mass":32}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"time_ref":30,"molar_mass_ref":2.016,"molar_mass":32}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/graham-effusion-time", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"time_ref": 30,
"molar_mass_ref": 2.016,
"molar_mass": 32
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.graham_effusion_time",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This capability computes t2 equals t1 times the square root of M2 over M1 deterministically, rejects a zero molar mass with a clear invalid_input error so notebooks never see Infinity, and returns JSON that homework checkers and lightweight chemistry helpers can pin in tests.
What Graham effusion time means and which inputs you must send
Send a positive time_ref for the reference gas in any coherent time unit you already use for the problem (seconds, minutes, or hours), the reference molar_mass_ref, and the second-gas molar_mass in the same molar-mass family (grams per mole or kilograms per mole). Aliases t1, effusion_time, t_ref, M1, M_ref, molar_mass_1, M2, M, and molar_mass_2 are accepted so forms and scripts can match textbook variable names.
How this calculator validates inputs and applies t2 = t1 √(M2/M1)
Send a JSON body with required time_ref, molar_mass_ref, and molar_mass. Every numeric field must be finite: missing required values, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. After validation the engine forms the ratio of the second molar mass to the reference molar mass, takes the positive square root to obtain the time ratio t2 over t1, multiplies by the reference time to obtain the second-gas effusion time, rounds every floating result to a stable decimal precision so the same input always yields the same JSON across JavaScript engines, and echoes the three inputs. The response includes time as t2, time_ratio as t2 over t1, rate_ratio as the matching rate one over rate two value under Graham’s law, formula always set to t2 equals t1 times sqrt of M2 over M1, and method always graham_effusion_time so downstream code can branch without sniffing shapes.
API usage, pricing, classroom workflows, and practical limits
Call the free in-browser graham effusion time calculator for homework checks, lecture demos, and quick hydrogen-versus-oxygen mental math without installing a thermodynamics package. Use the prepaid API when a tutoring platform, coding-assessment sandbox, curriculum generator, lab notebook helper, or gas-analysis pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with molar-mass tools when the next step is converting a chemical formula into M1 or M2, or with ideal-gas helpers when concentration and mean speed context are required around the same problem set. Choose molar-mass and time units consistently on both sides of the ratio so the solved second-gas time stays in the same time unit as time_ref and independent of whether you quote grams per mole or kilograms per mole. Authors shipping SDKs can map time into student-facing answer fields and time_ratio into comparison tables—the same two numbers learners write when they apply Graham’s law by hand on timed-effusion problems.
Integration use cases
Deterministic fixtures for chemistry tests
Pipelines that seed unit tests or interactive science demos can call a pure t2=t1√(M2/M1) oracle instead of reimplementing Graham arithmetic in every language.
Technical questions
How do I calculate the second gas effusion time with Graham’s law?
Send JSON with time_ref (t1), molar_mass_ref (M1), and molar_mass (M2). The response returns time as t2 = t1 × √(M2/M1), plus time_ratio and rate_ratio.